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Celestial Encounters: The Origins of Chaos and Stability (Princeton Science Library)

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Synopses & Reviews

Publisher Comments:

Celestial Encounters is for anyone who has ever wondered about the foundations of chaos. In 1888, the 34-year-old Henri Poincaré submitted a paper that was to change the course of science, but not before it underwent significant changes itself. "The Three-Body Problem and the Equations of Dynamics" won a prize sponsored by King Oscar II of Sweden and Norway and the journal Acta Mathematica, but after accepting the prize, Poincaré found a serious mistake in his work. While correcting it, he discovered the phenomenon of chaos.

Starting with the story of Poincaré's work, Florin Diacu and Philip Holmes trace the history of attempts to solve the problems of celestial mechanics first posed in Isaac Newton's Principia in 1686. In describing how mathematical rigor was brought to bear on one of our oldest fascinations--the motions of the heavens--they introduce the people whose ideas led to the flourishing field now called nonlinear dynamics.

In presenting the modern theory of dynamical systems, the models underlying much of modern science are described pictorially, using the geometrical language invented by Poincaré. More generally, the authors reflect on mathematical creativity and the roles that chance encounters, politics, and circumstance play in it.

Synopsis:

Celestial Encounters is for anyone who has ever wondered about the foundations of chaos. In 1888, the 34-year-old Henri Poincaré submitted a paper that was to change the course of science, but not before it underwent significant changes itself. "The Three-Body Problem and the Equations of Dynamics" won a prize sponsored by King Oscar II of Sweden and Norway and the journal Acta Mathematica, but after accepting the prize, Poincaré found a serious mistake in his work. While correcting it, he discovered the phenomenon of chaos.

Starting with the story of Poincaré's work, Florin Diacu and Philip Holmes trace the history of attempts to solve the problems of celestial mechanics first posed in Isaac Newton's Principia in 1686. In describing how mathematical rigor was brought to bear on one of our oldest fascinations--the motions of the heavens--they introduce the people whose ideas led to the flourishing field now called nonlinear dynamics.

In presenting the modern theory of dynamical systems, the models underlying much of modern science are described pictorially, using the geometrical language invented by Poincaré. More generally, the authors reflect on mathematical creativity and the roles that chance encounters, politics, and circumstance play in it.

Synopsis:

"An excellent book combining scientific integrity and popular appeal."--Steve Smale, City University of Hong Kong

Table of Contents

Preface and Acknowledgments

A Note to the Reader

1. A Great Discovery - And a Mistake

2. Symbolic Dynamics

3. Collisions and Other Singularities

4. Stability

5. KAM Theory

Notes

Bibliography

Index

Product Details

ISBN:
9780691005454
Author:
Diacu, Florin
Author:
Holmes, Philip
Publisher:
Princeton University Press
Location:
Princeton
Subject:
Applied
Subject:
Astrophysics & Space Science
Subject:
Chaotic Behavior in Systems
Subject:
Celestial mechanics
Subject:
Cosmogony
Subject:
Mathematics
Subject:
Physics
Subject:
History of Science and Medicine, Philosophy of Science
Subject:
Astronomy and Cosmology
Subject:
Physics-Astrophysics
Copyright:
Edition Description:
Trade paper
Series:
Princeton Science Library
Publication Date:
March 1999
Binding:
TRADE PAPER
Grade Level:
College/higher education:
Language:
English
Illustrations:
23 halftones 64 line illus.
Pages:
256
Dimensions:
9 x 6 in 12 oz

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Related Subjects

Science and Mathematics » Astronomy » General
Science and Mathematics » Mathematics » Applied
Science and Mathematics » Mathematics » Popular Chaos and Fractals
Science and Mathematics » Physics » Astrophysics

Celestial Encounters: The Origins of Chaos and Stability (Princeton Science Library) New Trade Paper
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$35.25 In Stock
Product details 256 pages Princeton University Press - English 9780691005454 Reviews:
"Synopsis" by , Celestial Encounters is for anyone who has ever wondered about the foundations of chaos. In 1888, the 34-year-old Henri Poincaré submitted a paper that was to change the course of science, but not before it underwent significant changes itself. "The Three-Body Problem and the Equations of Dynamics" won a prize sponsored by King Oscar II of Sweden and Norway and the journal Acta Mathematica, but after accepting the prize, Poincaré found a serious mistake in his work. While correcting it, he discovered the phenomenon of chaos.

Starting with the story of Poincaré's work, Florin Diacu and Philip Holmes trace the history of attempts to solve the problems of celestial mechanics first posed in Isaac Newton's Principia in 1686. In describing how mathematical rigor was brought to bear on one of our oldest fascinations--the motions of the heavens--they introduce the people whose ideas led to the flourishing field now called nonlinear dynamics.

In presenting the modern theory of dynamical systems, the models underlying much of modern science are described pictorially, using the geometrical language invented by Poincaré. More generally, the authors reflect on mathematical creativity and the roles that chance encounters, politics, and circumstance play in it.

"Synopsis" by , "An excellent book combining scientific integrity and popular appeal."--Steve Smale, City University of Hong Kong
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